Related papers: The moduli space of 4-dimensional nilpotent comple…
In this paper, the authors apply a stratification of moduli spaces of complex Lie algebras to analyzing the moduli spaces of nxn matrices under scalar similarity and bilinear forms under the cogredient action. For similar matrices, we give…
We obtain the functions that bound the dimensions of finite dimensional nilpotent associative or Lie algebras of class 2 over an algebraically closed field in terms of the dimensions of their commutative subalgebras. As a result, we also…
We investigate the moduli space of sheaves supported on space curves of degree 4 and having Euler characteristic 1. We give an elementary proof of the fact that this moduli space consists of three irreducible components.
Numerical characteristics of identities of finite-dimensional nonassociative algebras are studied. The main result is the construction of a four-dimensional simple unitary algebra with fractional PI-exponent strictly less than its…
We study a coarse moduli space of irreducible representations of the group of unipotent matrices of order $\mathbb{4}$ over the ring of integers which have finite weight. All such representations are known to be monomial. To describe a…
The paper concerns an analogue of the famous Schur multiplier in the context of associative algebras and a measure of how far its dimension is from being maximal. Applying a methodology from Lie theory, we characterize all…
Subsets of a matrix algebra over a field that are invariant under conjugation and contain the linear span of each two of their commuting elements are described. They obviously include the subsets of diagonalizable and nilpotent matrices. In…
We extend results on finite dimensional nilpotent Lie algebras to Leibniz algebras and counterexamples to others are found. One generator algebras are used in these examples and are investigated further.
We investigate Lie algebras endowed with a complex symplectic structure and develop a method, called \emph{complex symplectic oxidation}, to construct certain complex symplectic Lie algebras of dimension $4n+4$ from those of dimension $4n$.…
This is the addendum to the paper "On the Multiplicity Problem and the Isomorphism Problem for the Four Subspace Algebra" Communications in Algebra, 40:6 (2012), 2005-2036 (DOI: 10.1080/00927872.2011.570830). We give here the full proof of…
This article provides a complete description of the differential Gerstenhaber algebras of all nilpotent complex structures on any real six-dimensional nilpotent algebra. As an application, we classify all pseudo-K\"ahlerian complex…
We characterize those modular group algebras FG whose group of unitary units is locally nilpotent under the classical involution of FG.
In the present paper we give the full description of the Lie nilpotent group algebras which have maximal Lie nilpotency indices.
We characterize those nilpotent algebras of prime power order and finite type in congruence modular varieties that have infinitely many polynomially inequivalent congruence preserving expansions.
For most complex 9-dimensional filiform Lie algebra we find another non isomorphic Lie algebra that degenerates to it. Since this is already known for nilpotent Lie algebras of rank $\geq 1$, only the characteristically nilpotent ones…
A non-nilpotent variety of algebras is almost nilpotent if any proper subvariety is nilpotent. Let the base field be of characteristic zero. It has been shown that for associative or Lie algebras only one such variety exists. Here we…
We give a geometric classification of all $6$-dimensional nilpotent Tortkara algebras over $\mathbb C$
We study the structure of the supersymmetric moduli spaces of ${\cal N}=1$ and ${\cal N}=2$ supergravity theories in $AdS_4$ backgrounds. In the ${\cal N}=1$ case, the moduli space cannot be a complex submanifold of the K\"ahler field…
The moduli space of rank-n commutative algebras equipped with an ordered basis is an affine scheme B_n of finite type over Z, with geometrically connected fibers. It is smooth if and only if n <= 3. It is reducible if n >= 8 (and the…
We extend the classification of solvable Lie algebras with abelian nilradicals to classify solvable Leibniz algebras which are one dimensional extensions of an abelian nilradicals.